Probabilistic Symmetric Encryption Using Error-Correcting Codes
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current probabilistic symmetric encryption schemes lack mathematical arguments for proving computational security and require significant computational resources, failing to reconcile security proofs with practical implementation speed.
Innovation Solution
A method involving error-correcting codes and noise vectors is used, where a secret key is represented as a matrix, and a random vector is added to the encrypted code word, making it difficult for adversaries to decrypt, relying on the difficulty of the LPN problem for security.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If probabilistic symmetric encryption schemes using block encryption algorithms and operative modes are used, then encryption speed and practical implementation are improved, but mathematical arguments for proving computational security are lacking
Solution Approach 1:
The encryption scheme is segmented into two independent components: a block encryption algorithm (e.g., AES, DES) handled by a first entity, and a probabilistic transformation layer handled by a second entity. This segmentation allows each component to be optimized independently - the block encryption for speed and the probabilistic layer for security proofs, resolving the contradiction between encryption speed and computational security guarantees
Solution Approach 2:
A second entity acts as an intermediary between the plaintext and the block encryption algorithm. This intermediary applies a probabilistic transformation using public parameters and randomness, creating a layer that provides mathematical security proofs while allowing the underlying block encryption to operate at full speed without modification
2Reliability
If probabilistic symmetric encryption schemes are designed to provide computational security proofs, then security is improved, but computational resources and implementation complexity increase significantly
Solution Approach 1:
The scheme merges standard probabilistic encryption techniques (already widely implemented and understood) with conventional block encryption algorithms. By combining these two well-established approaches, the invention achieves computational security proofs without requiring entirely new complex algorithms, thus reducing implementation complexity while maintaining security guarantees
Solution Approach 2:
The probabilistic transformation layer uses universal building blocks (public parameters, randomness generation, simple mathematical operations) that can be implemented efficiently across different platforms. This multi-functional approach allows the same structure to provide both security proofs and work with various block encryption algorithms, reducing overall system complexity
Data Source
AI summary
The invention relates to a method of probabilistic symmetric encryption of a plaintext message element with the aid of a secret key that can be represented in the form of a matrix. It comprises an operation of encrypting the plaintext message element, with the aid of the matrix parametrized by a random vector, so as to obtain an encrypted message element coupled to the random vector. Furthermore, there is envisaged a step of encoding the plaintext message element as a code word with the aid of an error correcting code having a given correction capacity and a step of adding a noise vector. The error correcting code and the noise vector are adapted so that the Hamming weight of the noise vector is less than or equal to the correction capacity of the correcting code.